A number of problems pertinent to seismological and engineering interpretations of strong ground motions in earthquakes are studied. The main new results are as follows: (1) A new form of strong motion accelerogram (Spectrally Maximized Records or 'SMR') and its associated generalized spectrum are proposed for earthquake engineering use. Parameters (e.g., spectral, duration, peak amplitude) of horizontal-component strong-motion records at a given site generally depend significantly on the (arbitrary) azimuthal direction, often resulting in a crucially deficient description of these parameters if only a significant component is used. Combination of horizontal components using spectral maximization is shown to be effective in minimizing the difficulty. The spectra of the two horizontal components at each site are combined to maximize the resultant spectrum, independently or azimuthal orientation. SMRs of thirty-three important strong-motion accelerograms (including twelve New Guinea records) are then calculated from their corresponding spectra. (2) Statistical analysis of all accelerograms of the 1966 Parkfield earthquake, California and the 1952 Taft earthquake, California indicates that the usable long period of ground displacements obtained from double integration of accelerogram records are limited by two major sources of errors--human reading and base-line corrections. Usable long period limits are estimated to vary between 7 to 14 seconds depending on the individual earthquake. (3) It is shown that the integration of ragged functions such as strong motion accelerograms, by regular quadrature formulas, leads to significant errors. The conventional method of frequency domain integration also leads to indeterminacy of zero frequency information and distortion of the shape of the resulting integral. A modification of the conventional method of frequency domain integration was developed to avoid these deficiencies.